1. Field of the Invention
The present invention relates to a three-dimensional periodic structure, a method of producing the same, a high frequency element, and a high frequency apparatus that can be used in electronic parts.
2. Description of the Related Art
A periodic potential distribution in a solid crystal due to the nuclei exhibits interference of an electron wave having a wavelength that corresponds to the lattice constant. For example, when the wavelength of the electron wave is very close to the potential period of the crystal, reflection occurs by three-dimensional diffraction (Bragg diffraction). This phenomenon prevents the passage of electrons in a specific energy range. Thus, an electronic band gap, which is utilized in semiconductor devices, is formed.
Similarly, a three-dimensional structure having a periodically changing refractive index or dielectric constant exhibits interference of electromagnetic waves, thus blocking the electromagnetic waves in a specific frequency range. In this case, the forbidden band is called a photonic band gap and the three-dimensional structure is called a photonic crystal.
The effect of such a photonic crystal has been considered for use to provide a cut-off filter that prevents penetration of electromagnetic waves within a predetermined frequency band, or to provide a waveguide or a resonator by introducing a nonuniform part that disturbs the frequency to trap light or electromagnetic waves into the periodic structure. Applications such as ultra-low threshold lasers or electromagnetic highly directional antennas are also considered.
In general, in a photonic crystal, two types of standing waves are formed when the electromagnetic waves produce Bragg diffraction. FIG. 1 shows the two types of standing waves. Standing wave A has high energy at a low dielectric constant area of the wave vibration while standing wave B has high energy at a high dielectric constant area of the wave vibration. Waves having energy between the standing waves that split into two different modes cannot exist in the crystal, thereby producing the band gap. In order to broaden the band gap, the energy difference between the two standing waves is increased. This can be achieved by strengthening the contrast between the dielectric constants of two media to a high degree, or increasing the volume ratio of the media having the high dielectric constant.
The photonic crystal has a one-, two-, or three-dimensional structure. A three-dimensional structure is needed for a photonic band gap.
In order to provide a three-dimensional structure, Japanese Unexamined Patent Application Publication No. 10-335758 discloses “A three-dimensional periodic structure, a method of producing the same, and method of producing a film”, Japanese Unexamined Patent Application Publication No. 2000-329953 discloses “A photonic crystal and a method of producing the same”, Japanese Unexamined Patent Application Publication No. 2000-341031 discloses “A three-dimensional periodic structure and a method of producing the same”, Japanese Unexamined Patent Application Publication No. 2001-74954 discloses “A three-dimensional photonic crystal structure and a method of producing the same”, Japanese Unexamined Patent Application Publication No. 2001-215351 discloses “A periodic structure element having multiple dielectric constants, a method of designing the same, and a method of producing the same”, Japanese Unexamined Patent Application Publication No. 2000-158542 discloses “A structure, a multilayer structure, a method of producing the same, and an apparatus therefor”, and Japanese Unexamined Patent Application Publication No. 2000-258645 discloses “A three-dimensional periodic structure, a two dimensional structure, and a method of producing them”.
These three-dimensional periodic structures have been invented for application to various devices utilizing its photonic band gap. However, they do not suggest an electrode arrangement of the three-dimensional periodic structure. Also, they do not suggest applications for a waveguide in the microwave or millimeter wave range. When these three-dimensional periodic structures are used to construct a transmission path, the path becomes undesirably large.